Boundary Layer Modeling using Inflation Layers

In contemporary Computational Fluid Dynamics, for practicing engineers and students, there lies an essential need for the know-how of “making a mesh better” to capture gradient information especially at the fluid-surface boundaries. Modeling the boundary layer becomes extremely important. Visualization of the mainstream flow is, of course, vital to understand the flow behavior. However to obtain a fairly accurate solution for a fluid flow problem, appropriate discretization or meshing of the fluid domain at the boundary layer holds the key.

What is Boundary Layer?

From theoretical fluid mechanics, we know that gradients of velocity and temperature exist within the boundary layer (Wikipedia). Obviously the fluid that is immediately in contact with the boundary will have the same velocity as the boundary. As we move away from the boundary, the velocity of the successive layers of the fluid will increase. Within the boundary layer, shear stresses are developed between layers of fluid moving at different velocities because of viscosity and the interchange of momentum as a result of turbulence. This can cause movement of fluid particles from one layer to the other. In all such flows where “the wall” participation brings considerable changes in the fluid flow, we observe that there is a non-linear variation in the velocity profile normal to the flow direction.

Typical profile of a boundary layer

Without accurately capturing these effects at the boundary, you wouldn’t have an accurate solution to such fluid flow problems. Hence, to ensure that you get a fairly accurate result, I will provide recommendations for meshing at boundaries.

Boundary Layer – Key Meshing Recommendations

Typically, the best way to capture effects in the boundary layer is by accommodating higher number of cells in the direction normal to the fluid flow. For mainstream flow, I wouldn’t expect gradients to change much. Hence I recommend reducing the mesh intensity in the flow direction. Within the boundary layer, I would suggest you to have elements with high aspect ratios (up to 100-1000); you can stack them in the direction normal to the wall.

You will need to choose element types that can be stacked one over the other. By doing so, you can marginally save the number of grid cells and time required for the computation. Apart from the conserving the mesh count, it is extremely important to model the boundary layer with sufficiently high quality of meshing elements. You will agree that a poor quality mesh will obviously result in a commensurate accuracy of the solution.

Modeling the Boundary Layer in ANSYS

In ANSYS Fluent, you can achieving cell/element stacking in the direction normal to the boundary using a feature called Inflation. Essentially, you can inflate the mesh with several layers from the surface of the boundary until you cover the boundary layer thickness fully. Tetrahedral elements, when subjected to high aspect ratios, suffer from poor geometric quality. In contrast, Prism elements, due to very high geometric anisotropy, even if they are subject to high aspect ratios, show no deterioration in the geometric quality.

Now, I will compare using prism elements to model the boundary layer instead of tetrahedral elements. Towards the end, I will draw comparison between these two types of elements.

Hybrid mesh with prism and tetrahedral elements

For a sample geometry, I have utilized the inflation feature to setup the growth of five inflation layers from the surface of the boundary. As you can see, prism elements are stacked over one another (inflated) in order to capture the boundary layer effects.

If the number of layers are specified as three, the meshing tool grows three layers of prism elements. Beyond the inflation layers, the rest of the fluid domain is meshed with tetrahedral elements. Therefore, the end result will be a hybrid mesh of prism and tetrahedral elements. You can control the inflation layers with parameters like growth rate.

The Benefits

Without InflationWith Inflation

In the velocity contour plots, you can see the solution to the fluid flow problem with and without use of inflation. If you notice, the velocity gradients at the boundary are captured quite well when inflation is used. Do you work with applications that involve highly turbulent flows? In such cases, mesh inflation at the boundaries becomes extremely crucial.

In addition to capturing the boundary layer effects accurately, inflation also contributes to lesser element count and computational time. Considering this, I would advise you to use inflation for any wall bounded flow.

In this article, I explained the importance and the approach the use Inflation in the boundary layer. In my next article, I will describe ways to control the growth of the inflation layers using specific application(s).

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